Charge and force on a conductive sphere between two parallel electrodes: A Stokesian dynamics approach

Abstract

We present an accurate and efficient method to compute the electrostatic charge and force on a conductive sphere between two parallel electrodes. The method relies on a Stokesian dynamics-like approach, in which the capacitance tensor is divided into two contributions: (1) a far field contribution that captures the long range, many body interactions between the sphere and the two electrodes and (2) a near field contribution that captures the pairwise interactions between nearly contacting surfaces. The accuracy of this approach is confirmed by comparison to "exact" numerical results obtained by finite element modeling. From the capacitance tensor, we derive the charge and dipole moment on the sphere, the electrostatic free energy of the system, and the electrostatic force on the sphere. These quantities are used to describe the dynamics of micron-scale particles oscillating within a viscous dielectric liquid between two parallel electrodes subject to constant voltage. Simulated particle trajectories agree quantitatively with those captured experimentally by high speed imaging. © 2014 AIP Publishing LLC.